IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v145y2021ics0960077921000424.html
   My bibliography  Save this article

Projections and fractional dynamics of COVID-19 with optimal control strategies

Author

Listed:
  • Nabi, Khondoker Nazmoon
  • Kumar, Pushpendra
  • Erturk, Vedat Suat

Abstract

When the entire world is eagerly waiting for a safe, effective and widely available COVID-19 vaccine, unprecedented spikes of new cases are evident in numerous countries. To gain a deeper understanding about the future dynamics of COVID-19, a compartmental mathematical model has been proposed in this paper incorporating all possible non-pharmaceutical intervention strategies. Model parameters have been calibrated using sophisticated trust-region-reflective algorithm and short-term projection results have been illustrated for Bangladesh and India. Control reproduction numbers (Rc) have been calculated in order to get insights about the current epidemic scenario in the above-mentioned countries. Forecasting results depict that the aforesaid countries are having downward trends in daily COVID-19 cases. Nevertheless, as the pandemic is not over in any country, it is highly recommended to use efficacious face coverings and maintain strict physical distancing in public gatherings. All necessary graphical simulations have been performed with the help of Caputo–Fabrizio fractional derivatives. In addition, optimal control strategies for fractional system have been designed and the existence of unique solution has also been showed using Picard–Lindelof technique. Finally, unconditional stability of the fractional numerical technique has been proved.

Suggested Citation

  • Nabi, Khondoker Nazmoon & Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Projections and fractional dynamics of COVID-19 with optimal control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921000424
    DOI: 10.1016/j.chaos.2021.110689
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921000424
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110689?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nabi, Khondoker Nazmoon, 2020. "Forecasting COVID-19 pandemic: A data-driven analysis," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Jajarmi, Amin & Baleanu, Dumitru, 2018. "A new fractional analysis on the interaction of HIV with CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 221-229.
    3. Sene, Ndolane, 2020. "SIR epidemic model with Mittag–Leffler fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    4. Nabi, Khondoker Nazmoon & Abboubakar, Hamadjam & Kumar, Pushpendra, 2020. "Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Moualkia, Seyfeddine, 2023. "Mathematical analysis of new variant Omicron model driven by Lévy noise and with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Kumar, Pushpendra & Govindaraj, V. & Erturk, Vedat Suat, 2022. "A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Kumar, Pushpendra & Erturk, Vedat Suat & Murillo-Arcila, Marina, 2021. "A complex fractional mathematical modeling for the love story of Layla and Majnun," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    4. Khan, Muhammad Altaf & Atangana, Abdon, 2022. "Mathematical modeling and analysis of COVID-19: A study of new variant Omicron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    5. Kim, Sangkwon & Kim, Junseok, 2021. "Robust and accurate construction of the local volatility surface using the Black–Scholes equation," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. Khan, Hasib & Ibrahim, Muhammad & Abdel-Aty, Abdel-Haleem & Khashan, M. Motawi & Khan, Farhat Ali & Khan, Aziz, 2021. "A fractional order Covid-19 epidemic model with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    7. Alberto Olivares & Ernesto Staffetti, 2021. "Optimal Control Applied to Vaccination and Testing Policies for COVID-19," Mathematics, MDPI, vol. 9(23), pages 1-22, December.
    8. Kumar, Pushpendra & Erturk, Vedat Suat & Yusuf, Abdullahi & Kumar, Sunil, 2021. "Fractional time-delay mathematical modeling of Oncolytic Virotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    9. Chatterjee, Amar Nath & Ahmad, Bashir, 2021. "A fractional-order differential equation model of COVID-19 infection of epithelial cells," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    10. Jiraporn Lamwong & Napasool Wongvanich & I-Ming Tang & Puntani Pongsumpun, 2023. "Optimal Control Strategy of a Mathematical Model for the Fifth Wave of COVID-19 Outbreak (Omicron) in Thailand," Mathematics, MDPI, vol. 12(1), pages 1-31, December.
    11. Chaharborj, Sarkhosh Seddighi & Nabi, Khondoker Nazmoon & Feng, Koo Lee & Chaharborj, Shahriar Seddighi & Phang, Pei See, 2022. "Controlling COVID-19 transmission with isolation of influential nodes," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    12. Ullah, Mohammad Sharif & Higazy, M. & Ariful Kabir, K.M., 2022. "Modeling the epidemic control measures in overcoming COVID-19 outbreaks: A fractional-order derivative approach," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    13. Tsvetkov, V.P. & Mikheev, S.A. & Tsvetkov, I.V. & Derbov, V.L. & Gusev, A.A. & Vinitsky, S.I., 2022. "Modeling the multifractal dynamics of COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    14. Castillo, Oscar & Melin, Patricia, 2021. "A new fuzzy fractal control approach of non-linear dynamic systems: The case of controlling the COVID-19 pandemics," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chaharborj, Sarkhosh Seddighi & Nabi, Khondoker Nazmoon & Feng, Koo Lee & Chaharborj, Shahriar Seddighi & Phang, Pei See, 2022. "Controlling COVID-19 transmission with isolation of influential nodes," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Kumar, Pushpendra & Govindaraj, V. & Erturk, Vedat Suat, 2022. "A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Nabi, Khondoker Nazmoon & Abboubakar, Hamadjam & Kumar, Pushpendra, 2020. "Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Asamoah, Joshua Kiddy K. & Owusu, Mark A. & Jin, Zhen & Oduro, F. T. & Abidemi, Afeez & Gyasi, Esther Opoku, 2020. "Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Basnarkov, Lasko, 2021. "SEAIR Epidemic spreading model of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    6. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    7. Deniz, Sinan, 2021. "Optimal perturbation iteration method for solving fractional FitzHugh-Nagumo equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. Fawwaz Tawfiq Awamleh & Ala Nihad Bustami, 2022. "Examine the Mediating Role of the Information Technology Capabilities on the Relationship Between Artificial Intelligence and Competitive Advantage During the COVID-19 Pandemic," SAGE Open, , vol. 12(3), pages 21582440221, August.
    9. Ullah, Mohammad Sharif & Higazy, M. & Kabir, K.M. Ariful, 2022. "Dynamic analysis of mean-field and fractional-order epidemic vaccination strategies by evolutionary game approach," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    10. Chang, Yiming & Tao, YinYing & Shan, Wei & Yu, Xiangyuan, 2023. "Forecasting COVID-19 new cases through the Mixed Generalized Inverse Weibull Distribution and time series model," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    11. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
    12. Chatterjee, Amar Nath & Ahmad, Bashir, 2021. "A fractional-order differential equation model of COVID-19 infection of epithelial cells," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    13. Razminia, Kambiz & Razminia, Abolhassan & Baleanu, Dumitru, 2019. "Fractal-fractional modelling of partially penetrating wells," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 135-142.
    14. Kumar, Pushpendra & Erturk, Vedat Suat & Yusuf, Abdullahi & Kumar, Sunil, 2021. "Fractional time-delay mathematical modeling of Oncolytic Virotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    15. Du, Feifei & Lu, Jun-Guo, 2021. "New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    16. Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Environmental persistence influences infection dynamics for a butterfly pathogen via new generalised Caputo type fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    17. Higazy, M., 2020. "Novel fractional order SIDARTHE mathematical model of COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    18. Omame, Andrew & Abbas, Mujahid & Abdel-Aty, Abdel-Haleem, 2022. "Assessing the impact of SARS-CoV-2 infection on the dynamics of dengue and HIV via fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    19. Jajarmi, Amin & Yusuf, Abdullahi & Baleanu, Dumitru & Inc, Mustafa, 2020. "A new fractional HRSV model and its optimal control: A non-singular operator approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    20. Pang, Denghao & Jiang, Wei & Liu, Song & Jun, Du, 2019. "Stability analysis for a single degree of freedom fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 498-506.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921000424. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.